Buck Rogers is probably on the right track:
a. Stbd engine swallows a number of large birds and stops very suddenly due to severe rotational imbalance.
b. Side-Torque generated by this seizure slews that engine and its fuse-pin, upon reaching its design limit, lets go. Engine departs cleanly.
c. With the other engine under high power, and now due to great weight, lift and drag disparities, aircraft commences severe yaw (and roll and pitchdown/IAS increase) - imposing side-forces beyond design limit upon the vertical fin (which separates cleanly)
d. Aircraft "winds up" in its spiral dive with rapidly increasing asymmetric g and roll-rate - causing other engine to also depart due to excessive lateral loads on remaining engine pylon.
The key here is the design strength limits of fuse pins and vertical fins, once subjected to severe out-of-axis forces. Not sure why rudder would have detached (if it did). Winglets may have been torn off due to the same lateral aerodynamic load exceedances.